An interesting idea, and quite possible (vim7's tabs show as clicky GUI tabs in gnome-terminal), but I don't see the benefit of doing this..
Using the follow ~/.screenrc shows "graphical" tabs:
startup_message off
vbell off
hardstatus alwayslastline
hardstatus string '%{gk}[ %{G}%H %{g}][%= %{wk}%?%-Lw%?%{=b kR}(%{W}%n*%f %t%?(%u)%?%{=b kR})%{= kw}%?%+Lw%?%?%= %{g}]%{=y C}[%d/%m %c]%{W}'
..which look like the following (after renaming the tabs using ctrl+a,a:
x http://img216.imageshack.us/img216/9401/picture4myi.png
You can scroll around in a screen session using "copy mode", by doing ctrl+a,[ and using the cursor keys (press Esc or ctrl+c to exit it)
You can also attach to the same screen session multiple times using the screen -x flag (rather than -r), so you could use any tabbed terminal emulator, and open one tab for each screen-window.
If you really did want to start implementing this - one option would be to look into modifying gnome-terminal, to copy the behaviour with vim's tabs for screen. Or, write your own screen client - you don't need to do anything as fragile sounding as scraping the terminal - there's a FIFO file in (usually) /tmp/uscreens/S-$USER/$PID.sessionname which I think is how screen communicates, and remember screen is open-source!